A VSS analysis of robot dynamics under Coulomb frictions and a proposal of inertia-only robots

Robot dynamics under static and Coulomb frictions are shown to be equivalent to a nonlinear position-dependent circuit including a set of on-off switches and can be analyzed as a VSS (variable structure system). It is shown that, under the existence of static and Coulomb frictions at each joint, an ordinary PD feedback with gravity compensation for setpoint position control leads to a trapping of motion at some immovable state within a finite time without attaining the given target position. On the contrary, by introducing regressors for uncertain parameters of gravity forces and Coulomb frictions it is possible to show that a proper update law of such regressors leads to global asymptotic stability of setpoint position control without incurring any offset. This fact suggests a proposal of robots subject to only the terms due to inertia, that is, a proposal of inertia-only robots (or gravity/friction-free robots)